Question

in the figure below, \\( \overline { y x } \\) is a bisector of \\( \overline { w z } \\). \\( \overline { w z } = 20 a \\). what is the length of \\( \overline { e z } \\)?

Explanation:

Step1: Recall the definition of a bisector

A bisector divides a segment into two equal parts.

Step2: Calculate the length of \( EZ \)

Since \( YX \) is a bisector of \( WZ \), then \( EW = EZ \). And \( WZ=EW + EZ \). Given \( WZ = 20a \), substituting \( EW = EZ \) into \( WZ=EW + EZ \) gives \( WZ=2EZ \). Solving for \( EZ \), we have \( EZ=\frac{WZ}{2}\). Substituting \( WZ = 20a \) into the formula, \( EZ=\frac{20a}{2}=10a \).

Answer:

A. \(10a\)